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A Modified Conjugate Gradient Projection Method for Constrained Monotone Equations with Applications

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  • Yaping Hu

    (Tianjin University of Science and Technology)

Abstract

This paper presents an enhanced Wei-Yao-Liu conjugate gradient projection algorithm, tailored for solving large-scale nonlinear convex constrained monotone equations. The algorithm’s search direction guarantees sufficient descent, while both the direction and line search are derivative-free, making it highly efficient for large-scale problems. We prove the algorithm’s global convergence under suitable assumptions and demonstrate its applicability to sparse signal reconstruction and blurry image recovery in compressive sensing. Numerical experiments validate the algorithm’s effectiveness, especially in large-scale scenarios, underscoring the advantages of its derivative-free design.

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  • Yaping Hu, 2025. "A Modified Conjugate Gradient Projection Method for Constrained Monotone Equations with Applications," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-22, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02820-3
    DOI: 10.1007/s10957-025-02820-3
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    References listed on IDEAS

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    1. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
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